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Being on the second year of the Teach First programme has been a revelation to me…about quite how insane last year was. This year is hellish hard work still, but my stress levels are around a tenth of what they were last year.

Something happened this week which caused me to reflect on the contrast between this year and last year. It was Thursday and I’d been rounding off a sequence of lessons on the area and circumference of circles with a task of designing Bilbo Baggins a new house (everything had to be round). It was a messy lesson – coloured card, scissors, compasses, pencils, calculators, glue, felt tips etc. everywhere. I’d lost track of time, and (as will be familiar to you all I’m sure) realised with three minutes of the lesson to go that the classroom needed to be tidied, I needed to get together the resources for my Year 12 class happening immediately afterwards across the school, had homework to give out and had five reports to sign. Eek.

So I got the class quiet, gave out (rather loose) instructions to tidy up, put everything back in the right drawer and pick up a copy of the homework. Then I busied myself signing reports, disconnecting my laptop and prepping for my next class.

2 1/2 minutes later I looked up to see an almost spotless classroom with Adelle (bless her!) just emerging from my cupboard having put away the felt tips for me. Mason had taken it upon himself to hand out homework, and students were just tucking their chairs in. Bliss.

My point here isn’t to put across how wonderful my year 10 class are (although they are pretty awesome). It’s the contrast with last year that is so instructive. I am not doing anything fundamentally different at the end of class from what I did last year. I am no more organised (in fact I’m less ‘on it’ than I was at this time last year). And yet things just work this year, whether that is getting students to tidy the classroom quickly, keeping students ‘on task’ in a lesson, or getting students to attend detentions.

So this post is really a word in the ear of Teach First subject mentors. Don’t judge your mentee too harshly if their classroom is a tip at the end of a lesson, you look through the classroom window and see students off task, or the pace of their lesson drops because they are demanding (and not getting) the attention of every student. Your mentee might be doing everything right, and might be working far harder than anyone else in the department, and yet because of their inexperience and the reaction of the kids, the impact of their efforts will be different to anyone else’s in the department. Part of this is down to the authority they portray in front of the students, but part of it is also down to the kids and their reactions to new teachers. Rest assured your mentee is probably killing themselves trying to get it right, and will reap the rewards (as will the rest of the department) next year. Please help them get that far.

In this video of a sample lesson, the teacher gains a nuanced understanding of individual pupils’ understanding or lack of understanding in relation to equivalent fractions. This is limited to particular pupils, although by asking a variety of pupils this assessment is broadened.

She also scaffolds pupils’ learning through her questions, particularly where an individual struggles to answer.

Pupils gain several things from the questions also: those answering the questions have to articulate their thinking clearly, and so develop their understanding; those listening gain an understanding of how their peers tackle a question; for those who aren’t sure, the scaffolding questions point them in the right direction to be able to find an answer.

In this and in other videos, the teacher manages transitions very carefully, signalling to the pupils when she wants them to move on and reassuring them that they’ll have time to complete something later if they need to. One thing I would do differently is that she tends to ask pupils if they need more time and then move on regardless – either don’t ask or listen to the answer.

She involves pupils, both by getting them to answer questions and by getting them to come up to the board. This could be even better if she used mini whiteboards to check everyone’s answers to every question.

She was assessing pupils throughout, through: direct questioning, monitoring pupils answers whilst on task, asking them to explain why something was or wasn’t the case and picking up on misconceptions. Crucially, where a pupil didn’t get something right she asked them to have a look again.

To help pupils’ learning in the lesson I think I would have carried out an experiment on one of the probabilities that they found difficult to see if it was an estimated probability, such as the pin dropping. Doing so would have made the concept more real I think.

If I was working with a particular pupil who struggled, I would start by trying to pin down what they did understand i.e. did they understand the concepts of equally likely probabilities? and then build on this. I would try to use props e.g. a coin, and test out with them whether a coin toss was equally likely, and contrast this with a pin-head. I would use a scaffolding approach to push the limits of their knowledge, remaining positive and optimistic to encourage them to stretch themselves.

In this phase the teacher very clearly sets out the lesson objective for the lesson, and gives a very clear description of estimated probabilities. She asks pupils questions to scaffold learning towards the objective, although she very much controls the outcomes of this learning and doesn’t always build on the questions.

If I was to design a consolidation phase for this lesson, I think I would have introduced the topic in the same way, but then starting from the idea of the survey, I would have put up two sets of survey results, and got pupils to work through them and work out that they were different. I would then ask them what the probability of picking pizza is, to expose the idea that there isn’t a single probability. I would then ask what pupils could do to get a probability, eliciting the idea of an estimate. Finally, I would ask what would be a sensible way to get an estimate from the two sets of data, linking the idea to averages.

This would finally lead into a clear description of the key words ‘estimated probabilities’, which would come after we’d gone through the concept together.

This lesson starter is effective because: it builds on and cements previous learning; it is reasonably high-paced; it involves all pupils; the instructions are reasonably clear and logical.

Preparation for this activity consisted mainly of creating the powerpoint slide, and in preparing instructions carefully.

It engages pupils’ attention well, because each of them have something to do. It would have been even better if there was a competitive or fun element to it. For example, if I was to do this activity I would turn it into a code-breaking activity also, using a cipher based on equivalent fractions.

The teacher regularly mentioned the time left, which had the impact of keeping pupils on-task, and encouraging them to try to finish.

The teacher also encouraged discussion between pupils, both initially and once they had finished, to check answers. This had the impact of encouraging collaboration and explanation (‘can you convince the other person why you’re right’) as well as encouraging independent learning for those who had finished, by checking their own answers.

I saw two lessons recently that had very different learning outcomes. In the first, pupils were clearly confused by the teacher, and the little that they learnt was from one another not the class teacher. The reason for this was at least threefold: her explanations were poorly planned and thus illogical; her mathematics knowledge was shaky; and her diagrams and examples were unclear and/or ambiguous.

By contrast, in the best maths lessons I saw, the planning was ‘invisible’. This was partly because the teacher was very experienced, but also partly because his knowledge of the topic and likely misconceptions was very secure.